X-ray computed tomography (CT) is performed by acquiring multiple one- or two-dimensional (1D or 2D) radiographs of a multi-dimensional sample from a range of different viewing angles that make up a single “scan”. From this set of 1D or 2D projection images, a multi-dimensional (2D or 3D) image of the sample can be reconstructed, showing the 2D or 3D spatial distribution of X-ray linear attenuation coefficient within the sample. Non-destructive inspection of complex internal structures using high-resolution X-ray CT (micro-CT) is rapidly becoming a standard technique in fields such as materials science, biology, geology, and petroleum engineering. Historically, CT has been used solely to image static samples. An exception is medical imaging, where patient movement is often unavoidable, particularly when imaging moving organs like the heart or the lungs. Dynamic CT in the medical context refers to imaging techniques which attempt to correct for movements such as a heartbeat, and forming a high-quality static image by removing the time-evolving component.
In contrast, for most micro-CT imaging, the dynamic behaviour (time evolution) of a 3D sample is of genuine interest, and not necessarily the result of involuntary or periodic movement. For example, the displacement of one immiscible fluid by another inside a porous material is a notoriously difficult problem in geology, both because of the complexity of the underlying physics and because standard experiments reveal very little about the micro-scale processes. Multiphase displacements are central to oil production since the manner in which water displaces oil in a geological formation determines whether, and how, oil can be economically extracted from that formation. In-place four-dimensional (4D) experimental data (3D over time) is extremely expensive to obtain and returns frustratingly little information; modelling studies are cheaper and provide more insight but lack true predictive power. Micro-scale comparisons between experiment and models are sorely needed for the modelling to be useful. Dynamic micro-CT is in principle a suitable modality for obtaining such 4D experimental data under laboratory conditions.
Conventional methods for performing CT reconstruction on radiographic image sets include filtered backprojection (FBP), Fourier inversion, and various iterative schemes such as algebraic reconstruction technique (ART), simultaneous iterative reconstruction technique (SIRT), and the related simultaneous algebraic reconstruction technique (SART). Such techniques all assume that (i) the sample is static, and (ii) the structure of interest within the sample falls entirely within the field of view of each radiograph. If the sample changes during acquisition, the radiographs will be inconsistent with one another, leading to artefacts and/or blurring of the reconstructed image. In practice this means that conventional CT imaging is restricted to situations where the sample is effectively static for the time it takes to acquire a full set of radiographs.
It has been proven that the CT reconstruction problem is mildly unstable with respect to high-frequency experimental noise, and that radiographs at approximately πN/2 viewing angles are required in order to accurately reconstruct a 3D image on an N3 grid of volume elements (voxels). As the acquisition time for each radiograph is proportional to N2, the maximum achievable time-resolution using conventional CT reconstruction techniques is proportional to N3. In other words, using conventional CT, the amount of time the sample must remain essentially static increases in proportion to the desired spatial resolution.
For lab-based CT systems, increasing spatial resolution means using a source that emits X-rays from a smaller region, meaning that an electron beam must be focussed onto a smaller region of target material. This fundamentally limits beam power since too much energy focussed onto too small a region vaporises the target material. In turn, this imposes a lower limit on the amount of time required to acquire a single radiograph at an acceptable signal-to-noise ratio (SNR). Consequently, a high-resolution, lab-based CT scan typically takes between four and fifteen hours, an unacceptable time resolution for imaging dynamically evolving samples of current interest.